Q.What value does each bubble on the plot at Figure 4.14 represent?
[Figure: Figure 4.14 is the scatter plot output of textbook Program 4-12: discount = np.array([10,20,30,40,50]) on the x-axis ('Discount offered') versus saleInRs = np.array([40000,45000,48000,50000,100000]) on the y-axis ('Sales in Rs'), drawn with plt.scatter(x=discount, y=saleInRs) and titled 'Sales Vs Discount'.]

Scatter Plot Interpretation

Imagine you are trying to see whether two things are connected. For instance, does spending more hours studying tend to go with higher exam scores? Or does a company's advertising budget seem to relate to its sales? A scatter plot is simply a picture that lets you look for such a connection.

You take two variables — one goes on the horizontal axis (the x-axis), the other on the vertical axis (the y-axis). Each person, item, or observation in your data becomes a single dot on the graph. The dot's position shows the value of both variables for that one case. If you have twenty students, you get twenty dots. That is all a scatter plot is: a cloud of points, each representing a pair of numbers.

What You Are Looking For

When you interpret a scatter plot, you are asking one central question: Is there a pattern in how these two variables move together? The answer usually falls into one of three broad categories.

A positive relationship means that as one variable increases, the other also tends to increase. The dots roughly climb from bottom-left to top-right. For example, years of education and income often show this pattern — more education, higher income.

A negative relationship means that as one variable increases, the other tends to decrease. The dots slope downward from top-left to bottom-right. Think of the number of hours you spend watching television and your physical activity level — more TV, less movement.

No relationship means the dots are scattered randomly with no clear upward or downward trend. The two variables simply do not move together in any consistent way. For instance, the number of umbrellas you own and your height probably show no pattern at all.

Strength and Form

Beyond the direction (positive or negative), you also judge the strength of the relationship. If the dots are tightly clustered along a clear line, the relationship is strong. If they are widely spread out, the relationship is weak. A perfect straight line would mean a perfect relationship — rare in real data.

You also look at the form. Most relationships are roughly linear — the dots follow a straight-line pattern. But sometimes the pattern is curved. For example, as you increase the price of a product, sales might drop sharply at first, then level off. That is a non-linear relationship, and a scatter plot will show it as a curve rather than a straight line.

Outliers …